Trailing Zeros of Prime Product

CAT 2000 Slot 1 · QA · Easy · Number Systems

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Let SS be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all elements of SS. With how many consecutive zeros will the product end?

  1. A.

    1

  2. B.

    4

  3. C.

    5

  4. D.

    10

Answer

A

Explanation

Zeros at the end of a product come from pairs of 2×52 \times 5. Among prime numbers less than 100, 22 and 55 appear exactly once as prime factors. Thus, there is only one pair of (2,5)(2, 5), which means the product ends in exactly 1 zero.

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